If you look at history, most of the advances in the last few centuries came out of western civilization. Western civilization was (is) predominately christian. But you can't really say its a causal relationship. In the middle ages, once the church discovered the ancient classics, they tried to apply that same philosophical rigor to construct a theology. The advances in philosophy during this period are undeniable, but in doing so, it kind of sowed the seeds of its own destruction. The enlightenment followed, and it became increasingly difficult to reconcile the god described in multiple fragmented and disparate accounts in the bible with the advances in human knowledge.
It's all about the Greeks. They were on to something. When the Romans discovered Greek culture, the Roman flourished. When the empire fell, Europe went retarded. But when Europe rediscoveed Greek ideas, as you point out, the renaissance happened and eventually the enlightenment.
There was an article linked around here somewhere that pointed out this is one of the problems Islamic countries are having getting out of their funk. They see the Greeks as degenerate pagans and perverts and turning to them for cultural/ intellectual inspiration is inthinkable. And so they are stuck in a perpetual and growing dark age.
The Arabic countries weren't always like this. I was visiting the musuem of science in Istanbul where it cataloged all the scientific/mathematic/engineering feats of the Arabs. They wrote lots of treatises on everything from medicine to astronomy. It was quite impressive. The concept of the number zero, whose importance cannot be understated, spread from the arabic world to the european world. I'm not really convinced on the whole religion being the antithesis of science. That's true for fundamentalist thinking, sure, but most people in church are not fundamentalist. They do not believe that earth is 6000 years old. The reason there are religious STEM people is because they can compartmentalize their beliefs, and they can compartmentalize their beliefs because for most people, the main purpose of religion is to create a community for people to make friends, socialize, and help one another out.
I've attended many churches in my lifetime, and with a lot of people I talked to, the vibe I got is that they don't reaaaaally believe any of this stuff. They believe that most of the stories in these ancient texts are allegorical in nature. On the spectrum of belief, most of them would be agnostic. One time I remember a pastor even giving a sermon about how converting people shouldn't be a big deal, and that we should all focus on being better people. Pretty sure he was one of the many people who attended seminary and became atheist/agnostic and continued delivering sermons to pay the bills. Now don't get me wrong, I also attended evangelical churches too, and they are pretty heavily anti evolution there. However for most people, believing in an inerrant bible is untenable.